Question

without actual division find which of the following fraction are terminating decimal :9/25

Answer 1

9/25
9/5²
The fractions having the denominator of the form 2 to the power m×5 to the power n have terminating expansion.
the factors of the denominator are 5² so it will have a terminating expansion

Answer 2

9/25 is a terminating decimal and its value is 0.36.

Given:

The fraction 9/25.

To Find:

To determine whether 9/25 is terminating or not.

Solution:

A fraction is said to be a terminating decimal if :

i) The denominator is a multiple or power of 2.

ii) The denominator is a multiple or power of 5.

iii) The denominator is a multiple or power of 2 and 5.

We know that powers of 10 are the product of powers of 2 and 5, i.e. $10^{n} = (2^{n} )(5^{n} )$ and hence, is a terminating decimal.

Now, we have to check whether the fraction 9/25 is terminating or not.

The denominator 25 = 5², is a power of 5 and hence, by the above conditions, 9/25 is a terminating decimal.

Another way to find whether the given fraction is terminating or not is by making the denominator in powers of 10.

Now, 9/25 = (9 x 4)/(25 x 4) = 36/100 = 0.36

Hence 9/25 is a terminating decimal and its value is 0.36.

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